Question

3. Bob the Builder wants to earn an annual rate of 10% on his investments,

how much (to the
nearest cent) should he pay for a note that will be worth $3,000 in 9 months?

Answer 1

He should pay $2,790.7.

Explanation:

This is a simple interest problem.

The simple interest formula is given by:

`E = P*I*t`

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time, in years.

After t years, the total amount of money is:

`T = E + P`

In this question:

Rate of 10%, so I = 0.1.

9 months, so
`t = (9)/(12) = 0.75`

How much should he pay for a note that will be worth $3,000 in 9 months?

We have to find P for which T = 3000. So

`T = E + P`

`3000 = E + P`

`E = 3000 - P`

Then

`E = P*I*t`

`3000 - P = P*0.1*0.75`

`1.075P = 3000`

`P = (3000)/(1.075)`

`P = 2790.7`

He should pay $2,790.7.